Thermomechanical Model of an Impermeable Porous Medium with a Chemically Active Filler

摘要

A self-consistent mathematical model describing the thermomechanical behavior of an elastic medium, which contains voids filled with a chemically active substance, is considered. The behavior of the medium is described by thermomechanical equations. Processes in the pores are described by a lumped model which allows for energy release, chemical reactions, and conditions of phase equilibrium. The model makes it possible to take into account an arbitrary number of components, which can be in solid and three mobile phases (liquid gaseous, liquid hydrocarbon, and aqueous phases). The distribution of components between phases is obtained using a thermodynamically consistent technique under assumption that any mobile component can be present in any mobile phase. In order to describe the thermodynamic behavior of the components with allowance for phase transitions, cubic equations of state are used, which are rather common in engineering practice. An algorithm based on a combination of domain decomposition method and physical splitting approach is proposed for the numerical solution of the model system of equations.